Answered: The machine element shown is fabricated…

The machine element shown is fabricated from steel. Determine center of mass. ( The density of steel is 7850 kg/m3.) ว ง C 40 mm 40 mm -20 mm 20 mm- 80 mm 60 mm Z 40 mm

Essentials of Business Analytics (MindTap Course List)

2nd Edition

ISBN:9781305627734

Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Chapter13: Nonlinear Optimization Models

Section: Chapter Questions

Problem 3P: Let S represent the amount of steel produced (in tons). Steel production is related to the amount of...

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The machine element shown is fabricated
from steel. Determine center of mass. (
The density of steel
is 7850 kg/m3.)
ว
ง
C
40 mm
40 mm
-20 mm
20 mm-
80 mm
60 mm
Z
40 mm

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Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function: S = 20 L0.30 C 0.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 50,000 tons of steel at minimum cost. If your answer is zero, enter “0”. Min L + C s.t. L0.30 C 0.70 L, C (b) Solve the optimization problem you formulated in part a. Hint: When using Excel Solver, start with an initial L > 0 and C > 0. Do not round intermediate calculations. Round your answers to the nearest whole number. L = C = Cost = $
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